mirror of https://github.com/CGAL/cgal
replaced '\ccPureGlobalScope' by 'CGAL::' in C++ arguments of '\cc...' macros
This commit is contained in:
Sven Schönherr
parent
13d2d38600
commit
e1bf76e050
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@ -32,8 +32,7 @@ $P=\{p\}$.
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An inclusion-minimal subset $S$ of $P$ with $ma(S)=ma(P)$ is called a
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\emph{support set}, the points in $S$ are the \emph{support points}.
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A support set has size at most $d+2$, and all its points lie on the
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boundary of $ma(P)$. In general, neither the support set nor its size
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are necessarily unique.
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boundary of $ma(P)$. In general, the support set is not necessarily unique.
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The underlying algorithm can cope with all kinds of input, e.g.~$P$ may be
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empty or points may occur more than once. The algorithm computes a support
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@ -186,18 +185,21 @@ two-, three-, and $d$-dimensional \cgal~kernel, respectively.
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\ccMemberFunction{ Point center( ) const;}{
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returns the center of \ccVar.
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\ccPrecond \ccVar\ is not empty and an implicit conversion
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from \ccc{ET} to \ccc{RT} must be available.}
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\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
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available.
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\ccPrecond \ccVar\ is not empty.}
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\ccMemberFunction{ FT squared_inner_radius( ) const;}{
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returns the squared inner radius of \ccVar.
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\ccPrecond \ccVar\ is not empty and an implicit conversion
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from \ccc{ET} to \ccc{RT} must be available.}
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\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
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available.
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\ccPrecond \ccVar\ is not empty.}
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\ccMemberFunction{ FT squared_outer_radius( ) const;}{
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returns the squared outer radius of \ccVar.
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\ccPrecond \ccVar\ is not empty and an implicit conversion
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from \ccc{ET} to \ccc{RT} must be available.}
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\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
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available.
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\ccPrecond \ccVar\ is not empty.}
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\medskip
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\ccGlueBegin
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@ -232,7 +234,7 @@ and the outer sphere. The boundary is the union of both spheres. By
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definition, an empty annulus has no boundary and no bounded side, i.e.~its
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unbounded side equals the whole space $\E_d$.
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\ccMemberFunction{ \ccPureGlobalScope Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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@ -262,8 +264,7 @@ unbounded side equals the whole space $\E_d$.
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\ccMemberFunction{ bool is_degenerate( ) const;}{
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returns \ccc{true}, iff \ccVar\ is degenerate, i.e.~if \ccVar\
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is empty or equal to a single point, equivalently if the
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number of support points is less than 2.}
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is empty or equal to a single point.}
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% -----------------------------------------------------------------------------
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\ccModifiers
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@ -303,6 +304,8 @@ An object \ccVar\ is valid, iff
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\item \ccVar\ is the smallest annulus containing its support set $S$, and
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\item $S$ is minimal, i.e.\ no support point is redundant.
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\end{itemize}
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\emph{Note:} In this release only the first item is considered by the
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validity check.
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\ccMemberFunction{ bool is_valid( bool verbose = false,
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int level = 0 ) const;}{
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@ -340,10 +343,10 @@ An object \ccVar\ is valid, iff
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_sphere_d<Traits>}\\[1ex]
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_sphere_d<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{Min_annulus_d_traits}
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% -----------------------------------------------------------------------------
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@ -355,10 +358,10 @@ constraints and a linear objective function. The solution is obtained
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using our exact solver for linear and quadratic
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programs~\cite{gs-eegqp-00}.
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The creation time is almost always linear in the number of points.
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Access functions and predicates take constant time, inserting a point
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might take up to linear time. The clear operation and the check for
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validity each take linear time.
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The creation time is almost always linear in the number of points. Access
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functions and predicates take constant time, inserting a point takes almost
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always linear time. The clear operation and the check for validity each
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take linear time.
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% -----------------------------------------------------------------------------
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@ -32,8 +32,7 @@ $P=\{p\}$.
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An inclusion-minimal subset $S$ of $P$ with $ma(S)=ma(P)$ is called a
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\emph{support set}, the points in $S$ are the \emph{support points}.
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A support set has size at most $d+2$, and all its points lie on the
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boundary of $ma(P)$. In general, neither the support set nor its size
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are necessarily unique.
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boundary of $ma(P)$. In general, the support set is not necessarily unique.
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The underlying algorithm can cope with all kinds of input, e.g.~$P$ may be
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empty or points may occur more than once. The algorithm computes a support
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@ -186,18 +185,21 @@ two-, three-, and $d$-dimensional \cgal~kernel, respectively.
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\ccMemberFunction{ Point center( ) const;}{
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returns the center of \ccVar.
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\ccPrecond \ccVar\ is not empty and an implicit conversion
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from \ccc{ET} to \ccc{RT} must be available.}
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\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
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available.
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\ccPrecond \ccVar\ is not empty.}
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\ccMemberFunction{ FT squared_inner_radius( ) const;}{
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returns the squared inner radius of \ccVar.
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\ccPrecond \ccVar\ is not empty and an implicit conversion
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from \ccc{ET} to \ccc{RT} must be available.}
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\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
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available.
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\ccPrecond \ccVar\ is not empty.}
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\ccMemberFunction{ FT squared_outer_radius( ) const;}{
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returns the squared outer radius of \ccVar.
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\ccPrecond \ccVar\ is not empty and an implicit conversion
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from \ccc{ET} to \ccc{RT} must be available.}
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\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
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available.
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\ccPrecond \ccVar\ is not empty.}
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\medskip
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\ccGlueBegin
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@ -232,7 +234,7 @@ and the outer sphere. The boundary is the union of both spheres. By
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definition, an empty annulus has no boundary and no bounded side, i.e.~its
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unbounded side equals the whole space $\E_d$.
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\ccMemberFunction{ \ccPureGlobalScope Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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@ -262,8 +264,7 @@ unbounded side equals the whole space $\E_d$.
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\ccMemberFunction{ bool is_degenerate( ) const;}{
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returns \ccc{true}, iff \ccVar\ is degenerate, i.e.~if \ccVar\
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is empty or equal to a single point, equivalently if the
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number of support points is less than 2.}
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is empty or equal to a single point.}
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% -----------------------------------------------------------------------------
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\ccModifiers
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@ -303,6 +304,8 @@ An object \ccVar\ is valid, iff
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\item \ccVar\ is the smallest annulus containing its support set $S$, and
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\item $S$ is minimal, i.e.\ no support point is redundant.
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\end{itemize}
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\emph{Note:} In this release only the first item is considered by the
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validity check.
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\ccMemberFunction{ bool is_valid( bool verbose = false,
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int level = 0 ) const;}{
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@ -340,10 +343,10 @@ An object \ccVar\ is valid, iff
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_sphere_d<Traits>}\\[1ex]
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_sphere_d<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{Min_annulus_d_traits}
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% -----------------------------------------------------------------------------
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@ -355,10 +358,10 @@ constraints and a linear objective function. The solution is obtained
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using our exact solver for linear and quadratic
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programs~\cite{gs-eegqp-00}.
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The creation time is almost always linear in the number of points.
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Access functions and predicates take constant time, inserting a point
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might take up to linear time. The clear operation and the check for
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validity each take linear time.
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The creation time is almost always linear in the number of points. Access
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functions and predicates take constant time, inserting a point takes almost
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always linear time. The clear operation and the check for validity each
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take linear time.
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% -----------------------------------------------------------------------------
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@ -183,7 +183,7 @@ reconstructing $me(P)$ from a given support set $S$ of $P$.
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By definition, an empty \ccRefName\ has no boundary and no bounded side,
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i.e.\ its unbounded side equals the whole space $\E_2$.
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\ccMemberFunction{ \ccPureGlobalScope Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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@ -290,7 +290,7 @@ anxious user that the traits class implementation is correct.
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\ccInclude{CGAL/IO/Window_stream.h}
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\ccFunction{ CGAL::Window_stream&
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operator << ( \ccPureGlobalScope Window_stream& ws,
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operator << ( CGAL::Window_stream& ws,
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const Min_ellipse_2<Traits>& min_ellipse);}{
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writes \ccVar\ to window stream \ccc{ws}.
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\ccRequire The window stream output operator is defined for
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@ -299,8 +299,8 @@ anxious user that the traits class implementation is correct.
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_circle_2<Traits>}\\[1ex]
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2_traits_2<R>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_circle_2<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_ellipse_2_traits_2<R>}\\[1ex]
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\ccRefIdfierPage{Min_ellipse_2_traits}
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% -----------------------------------------------------------------------------
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@ -50,12 +50,12 @@ Only default and copy constructor are required.
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% -----------------------------------------------------------------------------
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\ccHasModels
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2_traits_2<R>}
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\ccRefIdfierPage{CGAL::Min_ellipse_2_traits_2<R>}
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2<Traits>}
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\ccRefIdfierPage{CGAL::Min_ellipse_2<Traits>}
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% -----------------------------------------------------------------------------
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@ -132,7 +132,7 @@ whole plane $\E_2$.
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Each of the following predicates is only needed, if the corresponding
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predicate of \ccc{Min_ellipse_2} is used.
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\ccMemberFunction{ \ccPureGlobalScope Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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@ -52,7 +52,7 @@ The template parameter \ccc{R} is a model for \ccc{Kernel}.
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_ellipse_2<Traits>}\\[1ex]
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\ccRefIdfierPage{Min_ellipse_2_traits}
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% -----------------------------------------------------------------------------
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@ -183,7 +183,7 @@ reconstructing $me(P)$ from a given support set $S$ of $P$.
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By definition, an empty \ccRefName\ has no boundary and no bounded side,
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i.e.\ its unbounded side equals the whole space $\E_2$.
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\ccMemberFunction{ \ccPureGlobalScope Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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@ -290,7 +290,7 @@ anxious user that the traits class implementation is correct.
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\ccInclude{CGAL/IO/Window_stream.h}
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\ccFunction{ CGAL::Window_stream&
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operator << ( \ccPureGlobalScope Window_stream& ws,
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operator << ( CGAL::Window_stream& ws,
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const Min_ellipse_2<Traits>& min_ellipse);}{
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writes \ccVar\ to window stream \ccc{ws}.
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\ccRequire The window stream output operator is defined for
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@ -299,8 +299,8 @@ anxious user that the traits class implementation is correct.
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_circle_2<Traits>}\\[1ex]
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2_traits_2<R>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_circle_2<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_ellipse_2_traits_2<R>}\\[1ex]
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\ccRefIdfierPage{Min_ellipse_2_traits}
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% -----------------------------------------------------------------------------
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@ -50,12 +50,12 @@ Only default and copy constructor are required.
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% -----------------------------------------------------------------------------
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\ccHasModels
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2_traits_2<R>}
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\ccRefIdfierPage{CGAL::Min_ellipse_2_traits_2<R>}
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2<Traits>}
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\ccRefIdfierPage{CGAL::Min_ellipse_2<Traits>}
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% -----------------------------------------------------------------------------
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@ -132,7 +132,7 @@ whole plane $\E_2$.
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Each of the following predicates is only needed, if the corresponding
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predicate of \ccc{Min_ellipse_2} is used.
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\ccMemberFunction{ \ccPureGlobalScope Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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@ -52,7 +52,7 @@ The template parameter \ccc{R} is a model for \ccc{Kernel}.
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_ellipse_2<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_ellipse_2<Traits>}\\[1ex]
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\ccRefIdfierPage{Min_ellipse_2_traits}
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% -----------------------------------------------------------------------------
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@ -100,14 +100,14 @@ object.
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% -----------------------------------------------------------------------------
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\ccHasModels
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}
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\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}
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% -----------------------------------------------------------------------------
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@ -89,9 +89,9 @@ object.
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}\\[1ex]
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{Min_annulus_d_traits}
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% -----------------------------------------------------------------------------
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@ -89,9 +89,9 @@ object.
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}\\[1ex]
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
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\ccRefIdfierPage{Min_annulus_d_traits}
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% -----------------------------------------------------------------------------
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|
@ -89,9 +89,9 @@ object.
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{Min_annulus_d_traits}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
|
|
|||
|
|
@ -100,14 +100,14 @@ object.
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccHasModels
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
||||
|
|
|
|||
|
|
@ -89,9 +89,9 @@ object.
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{Min_annulus_d_traits}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
|
|
|||
|
|
@ -89,9 +89,9 @@ object.
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{Min_annulus_d_traits}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
|
|
|||
|
|
@ -89,9 +89,9 @@ object.
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Min_annulus_d_traits_3<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Min_annulus_d_traits_3<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{Min_annulus_d_traits}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
|
|
|||
|
|
@ -28,9 +28,8 @@ An object of the class \ccRefName\ represents the (squared) distance
|
|||
between two convex polytopes, given as the convex hulls of two finite point
|
||||
sets in $d$-dimensional Euclidean space $\E_d$. For point sets $P$ and $Q$
|
||||
we denote by $pd(P,Q)$ the distance between the convex hulls of $P$ and
|
||||
$Q$. Note that $pd(P,Q)$ can be degenerate, i.e.~$pd(P,Q)=0$ if the convex
|
||||
hulls of $P$ and $Q$ intersect, and $pd(P,Q)=\infty$ if $P$ or $Q$ is
|
||||
empty.
|
||||
$Q$. Note that $pd(P,Q)$ can be degenerate, i.e.~$pd(P,Q)=\infty$ if $P$
|
||||
or $Q$ is empty.
|
||||
|
||||
Two inclusion-minimal subsets $S_P$ of $P$ and $S_Q$ of $Q$ with
|
||||
$pd(S_P,S_Q)=pd(P,Q)$ are called \emph{pair of support sets}, the points in
|
||||
|
|
@ -192,18 +191,21 @@ using the two-, three-, and $d$-dimensional \cgal~kernel, respectively.
|
|||
|
||||
\ccMemberFunction{ Point realizing_point_p( ) const;}{
|
||||
returns the realizing point of $P$.
|
||||
\ccPrecond $pd(P,Q)$ is finite and an implicit conversion
|
||||
from \ccc{ET} to \ccc{RT} must be available.}
|
||||
\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
|
||||
available.
|
||||
\ccPrecond $pd(P,Q)$ is finite.}
|
||||
|
||||
\ccMemberFunction{ Point realizing_point_q( ) const;}{
|
||||
returns the realizing point of $Q$.
|
||||
\ccPrecond $pd(P,Q)$ is finite and an implicit conversion
|
||||
from \ccc{ET} to \ccc{RT} must be available.}
|
||||
\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
|
||||
available.
|
||||
\ccPrecond $pd(P,Q)$ is finite.}
|
||||
|
||||
\ccMemberFunction{ FT squared_distance( ) const;}{
|
||||
returns the squared distance of \ccVar, i.e.~$(pd(P,Q))^2$.
|
||||
\ccPrecond $pd(P,Q)$ is finite and an implicit conversion
|
||||
from \ccc{ET} to \ccc{RT} must be available.}
|
||||
\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
|
||||
available.
|
||||
\ccPrecond $pd(P,Q)$ is finite.}
|
||||
|
||||
\medskip
|
||||
\ccGlueBegin
|
||||
|
|
@ -256,7 +258,7 @@ using the two-, three-, and $d$-dimensional \cgal~kernel, respectively.
|
|||
|
||||
\ccMemberFunction{ bool is_degenerate( ) const;}{
|
||||
returns \ccc{true}, iff $pd(P,Q)$ is degenerate,
|
||||
i.e.~$pd(P,Q)=0$ or $pd(P,Q)=\infty$.}
|
||||
i.e.~$pd(P,Q)$ is not finite.}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
\ccModifiers
|
||||
|
|
@ -384,9 +386,9 @@ An object \ccVar\ is valid, iff
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Polytope_distance_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Polytope_distance_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Polytope_distance_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Polytope_distance_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Polytope_distance_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Polytope_distance_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{Polytope_distance_d_traits}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
|
|
|||
|
|
@ -28,9 +28,8 @@ An object of the class \ccRefName\ represents the (squared) distance
|
|||
between two convex polytopes, given as the convex hulls of two finite point
|
||||
sets in $d$-dimensional Euclidean space $\E_d$. For point sets $P$ and $Q$
|
||||
we denote by $pd(P,Q)$ the distance between the convex hulls of $P$ and
|
||||
$Q$. Note that $pd(P,Q)$ can be degenerate, i.e.~$pd(P,Q)=0$ if the convex
|
||||
hulls of $P$ and $Q$ intersect, and $pd(P,Q)=\infty$ if $P$ or $Q$ is
|
||||
empty.
|
||||
$Q$. Note that $pd(P,Q)$ can be degenerate, i.e.~$pd(P,Q)=\infty$ if $P$
|
||||
or $Q$ is empty.
|
||||
|
||||
Two inclusion-minimal subsets $S_P$ of $P$ and $S_Q$ of $Q$ with
|
||||
$pd(S_P,S_Q)=pd(P,Q)$ are called \emph{pair of support sets}, the points in
|
||||
|
|
@ -192,18 +191,21 @@ using the two-, three-, and $d$-dimensional \cgal~kernel, respectively.
|
|||
|
||||
\ccMemberFunction{ Point realizing_point_p( ) const;}{
|
||||
returns the realizing point of $P$.
|
||||
\ccPrecond $pd(P,Q)$ is finite and an implicit conversion
|
||||
from \ccc{ET} to \ccc{RT} must be available.}
|
||||
\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
|
||||
available.
|
||||
\ccPrecond $pd(P,Q)$ is finite.}
|
||||
|
||||
\ccMemberFunction{ Point realizing_point_q( ) const;}{
|
||||
returns the realizing point of $Q$.
|
||||
\ccPrecond $pd(P,Q)$ is finite and an implicit conversion
|
||||
from \ccc{ET} to \ccc{RT} must be available.}
|
||||
\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
|
||||
available.
|
||||
\ccPrecond $pd(P,Q)$ is finite.}
|
||||
|
||||
\ccMemberFunction{ FT squared_distance( ) const;}{
|
||||
returns the squared distance of \ccVar, i.e.~$(pd(P,Q))^2$.
|
||||
\ccPrecond $pd(P,Q)$ is finite and an implicit conversion
|
||||
from \ccc{ET} to \ccc{RT} must be available.}
|
||||
\ccRequire An implicit conversion from \ccc{ET} to \ccc{RT} is
|
||||
available.
|
||||
\ccPrecond $pd(P,Q)$ is finite.}
|
||||
|
||||
\medskip
|
||||
\ccGlueBegin
|
||||
|
|
@ -256,7 +258,7 @@ using the two-, three-, and $d$-dimensional \cgal~kernel, respectively.
|
|||
|
||||
\ccMemberFunction{ bool is_degenerate( ) const;}{
|
||||
returns \ccc{true}, iff $pd(P,Q)$ is degenerate,
|
||||
i.e.~$pd(P,Q)=0$ or $pd(P,Q)=\infty$.}
|
||||
i.e.~$pd(P,Q)$ is not finite.}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
\ccModifiers
|
||||
|
|
@ -384,9 +386,9 @@ An object \ccVar\ is valid, iff
|
|||
% -----------------------------------------------------------------------------
|
||||
\ccSeeAlso
|
||||
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Polytope_distance_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Polytope_distance_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{\ccPureGlobalScope Polytope_distance_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{CGAL::Polytope_distance_d_traits_2<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Polytope_distance_d_traits_3<R,ET,NT>}\\
|
||||
\ccRefIdfierPage{CGAL::Polytope_distance_d_traits_d<R,ET,NT>}\\[1ex]
|
||||
\ccRefIdfierPage{Polytope_distance_d_traits}
|
||||
|
||||
% -----------------------------------------------------------------------------
|
||||
|
|
|
|||
Loading…
Reference in New Issue